Sen. Dianne Feinstein’s bombshell accusation about the Central Intelligence Agency Tuesday set off a scramble on Capitol Hill — with Democrats and Republicans ignoring the usual party lines in response to her claim that the agency improperly interfered in a congressional investigation.

Feinstein (D-Calif.) won immediate backing from top Democrats like Majority Leader Harry Reid and Judiciary Committee Chairman Patrick Leahy while some Republicans, including Lindsey Graham and John McCain, began to echo her concerns.

But the chairwoman of the Senate Intelligence Committee also faced skepticism from Georgia’s Saxby Chambliss, the panel’s top Republican and Marco Rubio (R-Fla.), a member of the committee. Even Maryland’s Barbara Mikulski, a leading Democrat, said she wants more facts.

The unusual divisions underscore the complicated relationship between Capitol Hill and the nation’s spy agencies that first emerged after the Sept. 11 attacks and has only deepened in the wake of the Edward Snowden leaks.

“There’s disagreements as to what the actual facts are,” Chambliss said Tuesday. “What I’m hopeful for is that we will have a kind of study done on what happened so that people can find out what the facts are. Right now, we don’t know what the facts are.”

The latest dispute stems from an investigation conducted by Feinstein’s panel into Bush-era detention and interrogation programs. Setting off a political firestorm, Feinstein took to the Senate floor Tuesday to accuse the agency of putting up barriers to that probe, blasting CIA officials for potentially violating the Constitution in conducting an unauthorized search of her committee’s computers to turn up documents related to that inquiry.

Feinstein, who spoke to President Barack Obama about her concerns, said her panel will vote to declassify the report into the interrogation practices sometime this month, something that could embarrass the intelligence community.

“We’re not going to stop,” she said. “If the Senate can declassify this report, we will be able to ensure that an un-American, brutal program of detention and interrogation will never again be considered or permitted.”

CIA Director John Brennan forcefully pushed back against Feinstein’s allegations, prompting senators to begin calling for a larger investigation into the matter. But lawmakers have yet to coalesce around whether that means a special prosecutor or whether it should be done internally within the existing Senate process.

The intelligence panel convened Tuesday for a tense, two-hour classified meeting in the Senate Hart Office Building. As Feinstein shuttled out of the room following the session, Chambliss spoke briefly to reporters but gave little clarity on the panel’s next steps.

“We have some issues that have been discussed in the press and we’re looking at those issues from an internal standpoint very closely. We’re going to continue with our internal review and at the appropriate time we’ll have further statements to make,” Chambliss said, declining to take questions.

Reid, who has spoken to Brennan about the situation but said he “unequivocally” supports Feinstein, said an investigation isn’t in the immediate offing.

“Heads will roll,” Graham said if an investigation confirms Feinstein’s allegations. “If what they’re saying is true about the CIA, this is Richard Nixon stuff. This is dangerous to a democracy, heads should roll, people should go to jail, if it’s true,” Graham said. “The legislative branch should declare war on the CIA — if it’s true.”

“There needs to be an investigation of this whole situation,” McCain said. “It’s very disturbing.”

“This raises a very troubling set of questions,” said Sen. Ron Wyden (D-Ore.), a frequent critic of the vast domestic surveillance. “We are right at the heart of the issue of how Congress goes about effectively doing oversight.”

Indeed, many in Congress are preparing for a renewed debate over the separation of power between the legislative and executive branches of government — a field often reserved for Republicans to pummel what they see as overreach by the White House.

But not every Republican was ready to make that case on Tuesday.

Rubio, a potential presidential candidate, argued that Senate staff investigating the matter may not be blameless in the extraordinary tussle between the CIA and the Senate, pointing to allegations that the staff may have illegally accessed CIA documents. An agency lawyer has filed a criminal report to the Justice Department over the incident, something Feinstein said was meant to “intimidate” her committee.

“I’m concerned about it. I’m also concerned about the potential violations by our own staff. I think there are two sides of every story, and this calls for an independent impartial investigation,” Rubio said. “And I think you might find there is wrongdoing on both sides.”

Even though he usually works closely with Feinstein on intelligence matters, Chambliss immediately distanced himself from the California senator’s remarks — and refused to comment further about the serious allegations.

One of Chambliss’s closest friends, Tom Coburn of Oklahoma, who also serves on the panel, said “there’s a lot of the story that’s not out there.”

“I think we need to know more of the facts,” said Mikulski, the veteran Maryland Democrat who serves on the committee. Asked if she had come to the conclusion that the CIA may have committed a constitutional violation, as Feinstein suggested, Mikulski replied: “No, because I find right now that there are accusations … which is unfortunate, and I hope we can really have some more conclusions.”

The skeptical remarks of several Intelligence Committee members following Feinstein’s speech stood in clear contrast to civil libertarians who backed Feinstein and offered her allegations as just the latest example of how difficult it has become for Congress to oversee the sprawling U.S. intelligence apparatus.

“She was absolutely correct in what she said. I think the agency, as they have done in the past, would love not to talk about some of the things they’ve done,” said Leahy, the chamber’s most senior member. “She’s speaking the truth.”

“They have not answered her questions, which is I think totally unacceptable,” Senate Armed Services Chairman Carl Levin (D-Mich.) said of the CIA. “They’ve got to be answered, and the fact there is an ongoing investigation is no excuse for them not answering it. This is a government agency that has got to basically be straight with not only the American people but with [the Intelligence Committee.]”